XBee shield is an Arduino shield that an XBee can be plugged into. XBees often need a different power supply voltage than the MCU they are connected to, and also signal level shifting; circuitry on the shield takes care of this.

XBee Explorer is the name that Sparkfun Electronics gives its XBee breakout boards. An XBee breakout board is similar to a shield in that it accepts an XBee and may do level shifting and power supply regulation, but has a different form factor, so does not plug directly into an Arduino like a shield, but may be used with a breadboard instead. Several companies make XBee breakout boards.

ZigBee is one protocol that certain XBee families use. (ZigBee products are made by many other manufacturers as well.)